Fourier Analysis of Semistable Distributions

We consider the generalized convolution powers G _α ^*u (x) of an arbitrary semistable distribution function G _α (x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G _α ^(k,j)(x;u)=∂ ^k+j G _α ^*u (x)/∂ x ^k ∂ u ^j , x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in merge theorems from the domain of geometric partial attraction of semistable laws. An erratum to this article can be found at     

Time interval distributions of atoms in atomic beams

We report an experimental investigation of two-particle correlations between neutral atoms in a Hanbury Brown and Twiss experiment. Both an atom laser beam and a pseudo-thermal atomic beam are extracted from a Bose–Einstein condensate and the atom flux is measured with a single atom counter. We determine the conditional and the unconditional detection probabilities for the atoms in the beam and find good agreement with the theoretical predictions. PACS 03.75.Pp; 05.30.Jp; 07.77.Gx; 42.50.Pq     

Polarizability effect in metallic clusters

Langevin approach implemented in the inelastic cross-sections measured for the low-energy electrons colliding with metallic clusters points out that statical form of the polarizability dominate at energies less than 1.25 eV. The dynamical form comes into play at energies around 1.3 eV. The form of the polarizabilities indicates that polarizability of the metallic clusters is energy-dependent.     

Adhesion studies of latex film surfaces on the meso- and nanoscale

In this paper the effects of surface roughness and annealing temperature (T) of latex coating films on adhesion are discussed for the different stages of the film formation process. The surface free energy of latex films was assessed in terms of practical work of adhesion (W) (or adherence) using a custom-built adhesion-testing device (ATD), atomic force microscopy (AFM), and contact angle measurements. For preannealed latex films surface roughness averages (R_a) were determined from AFM height images and were related to the values of W obtained from ATD measurements at room temperature. The results obtained using these tests exhibiting surface behavior on different length scales indicate a dependence of the measured adhesion on surface roughness and temperature, as well as on the length scale of the measurements.First preannealed samples were studied, which were obtained by heat treatment above the respective glass transition temperatures (T_g). Increasing the temperature of preannealing resulted in a decrease of the adherence observed in ATD experiments at room temperature. However, on the nanoscale, using AFM, no significant variation of the adherence was observed. This observation can be explained by roughness arguments. Preannealing decreases roughness which results in lower adherence values measured by ATD while for essentially single asperity AFM experiments roughness has an insignificant effect. Specimens were also annealed over a constant period of time (90 min) at different temperatures. At the end of the heat treatment, adhesion was measured at the treatment temperature by ATD. The amplified effect of temperature observed in this case on adherence is attributed to the combination of roughness decrease and increasing test temperature. In a third set of experiments completely annealed samples were studied by ATD as well as by AFM as a function of temperature. With increasing T values ATD showed a decrease in adherence, which is attributed to a decreasing surface free energy of the annealed films at elevated T values. AFM, on the other hand, showed an opposite trend which is assigned to increasing penetration of the tip into the tip/wetting polymer samples versus increasing temperature. Finally, annealing isotherms as a function of time were investigated by ATD in situ at different temperatures. This last set of experiments allowed us to optimize annealing time and temperature to achieve complete curing.     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Markov processes associated with L p -resolvents and applications to stochastic differential equations on Hilbert space

We give general conditions on a generator of a C₀-semigroup (resp. of a C₀-resolvent) on L^p(E,μ), p ≥ 1, where E is an arbitrary (Lusin) topological space and μ a σ-finite measure on its Borel σ-algebra, so that it generates a sufficiently regular Markov process on E. We present a general method how these conditions can be checked in many situations. Applications to solve stochastic differential equations on Hilbert space in the sense of a martingale problem are given. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday     

Route stability in vehicle routing decisions: a bi-objective approach using metaheuristics

In this paper, we argue that vehicle routing solutions are often tactical decisions, that should not be changed too often or too much. For marketing or other reasons, vehicle routing solutions should be stable, i.e. a new solution (when e.g. new customers require service) should be as similar as possible to a solution already in use. Simultaneously however, this new solution should still have a good quality in the traditional sense (e.g. small total travel cost). In this paper, we develop a way to measure the difference between two vehicle routing solutions. We use this distance measure to create a metaheuristic approach that will find solutions that are “close” (in the solution space) to a given baseline solution and at the same time have a high quality in the sense that their total distance traveled is small. By using this approach, the dispatcher is offered a choice of Pareto-optimal solutions, allowing him to make a trade-off between changing his existing solution and allowing a longer travel distance. Some experiments are performed to show the effectiveness of the approach.     

A finite cutting plane method for facial disjunctive programs

This paper shows that any linear disjunctive program with a finite number of constraints can be transformed into an equivalent facial program. Based upon linear programming technique, a new, finite cutting plane method is presented for the facial programs.

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Zusammenfassung Die Arbeit zeigt, daß jedes lineare disjunktive Optimierungsproblem mit endlich vielen Restriktionen in ein äquivalentes Fazetten-Problem transformiert werden kann. Auf der Grundlage von linearer Optimierungstechnik wird für das Fazetten-Problem ein neues, endliches Schnittebenenverfahren vorgestellt.